This theorem was first proved by Augustin-Louis Cauchy in 1813 [1]}.
It is considered one of the most striking achievements of geometry.
It has a significant impact on the development of synthetic geometry and is well presented in
scientific [2]}, [3]}, [4]}, [5]}, [6]},
educational [7]}, [8]},
and popular science [9]}, [10]}, [11]}, [12]}
literature.
Of recent articles using or generalizing Theorem REF , we mention article [13]},
where the local rigidity of zonohedra is proved in \(\mathbb {R}^3\) ;
articles [14]}, [15]}, [16]}, where the rigidity of a polyhedron is proved in \(\mathbb {R}^3\) 
provided that it is homeomorphic to the sphere, torus or pretzel and all its faces are unit squares;
article [17]}, in which Theorem REF  carries over to the case of circular polytopes in
the 2-sphere \(\mathbb {S}^{2}\) ;
and article [18]}, in which a rather unexpected application of Theorem REF  is given to find
a sufficient condition for a convex polyhedron \(P\)  to realize by means of isometries of the ambient space \(\mathbb {R}^3\) 
all “combinatorial symmetries” of \(P\) , i. e., all maps of the natural development of \(P\)  onto itself that preserve edge lengths.
